<p><b>Abstract</b>—A bipartite concentrator is a single stage sparse crossbar switching device that can connect any <it>m</it> of its <it>n</it>≥<it>m</it> inputs to its <it>m</it> outputs, possibly without the ability to distinguish their order. Fat-and-slim crossbars were introduced recently to show that bipartite concentrators can be constructed with a minimum number of crosspoints for any number of inputs and outputs. We generalize these graphs to obtain bipartite concentrators with nearly a fixed fanout without altering their (<it>n</it><tmath>$-$</tmath><it>m</it> + 1)<it>m</it> crosspoint complexity. We also present an <it>O</it>(log <it>n</it>)-time algorithm to route arbitrary concentration assignments on this new family of fat-and-slim crossbars.</p>